Assessing clustering strategies for Gaussian mixture filtering of a subsurface contaminant model

​An ensemble-based Gaussian mixture (GM) filtering framework is studied in this paper in term of its dependence on the choice of the clustering method to construct the GM. In this approach, a number of particles sampled from the posterior distribution are first integrated forward with the dynamical model for forecasting. A GM representation of the forecast distribution is then constructed from the forecast particles. Once an observation becomes available, the forecast GM is updated according to Bayes' rule. This leads to (i) a Kalman filter-like update of the particles, and (ii) a Particle filter-like update of their weights, generalizing the ensemble Kalman filter update to non-Gaussian distributions. We focus on investigating the impact of the clustering strategy on the behavior of the filter. Three different clustering methods for constructing the prior GM are considered: (i) a standard kernel density estimation, (ii) clustering with a specified mixture component size, and (iii) adaptive clustering (with a variable GM size). Numerical experiments are performed using a two-dimensional reactive contaminant transport model in which the contaminant concentration and the heterogenous hydraulic conductivity fields are estimated within a confined aquifer using solute concentration data. The experimental results suggest that the performance of the GM filter is sensitive to the choice of the GM model. In particular, increasing the size of the GM does not necessarily result in improved performances. In this respect, the best results are obtained with the proposed adaptive clustering scheme.